4th International Conference on Computational Heat and Mass Transfer
Proceedings of 4th ICCHMT
May 17–20, 2005, Paris-Cachan, FRANCE
Paper number____
EDUCATION & TUTORIALS IN MODELING IN COMPUTATION HEAT
TRANSFER: FROM ELEMENTARY PROCESSES ON THE BASIS OF
COMPUTER LABORATORY TO THE INDUSTRIAL COMPLEXES
A.I. Fedyushkin*, V.I. Polezhaev, and V.P.Yaremchuk
The Institute for Problems in Mechanics, Russian Academy of Sciences,
Prospect Vernadskogo 101, building 1, Moscow, 119526, Russia
*
Correspondence author: Phone: +7 095 4343283; Fax: +7 095 9382048; E-mail: fai@ipmnet.ru
ABSTRACT
A goal of the paper is to point on the steps
of training the students from using of the
computer laboratory for initial stage of the
education of the convective heat/mass
transfer on the basis of Navier-Stokes
equation till usage of professional industrial
CFD codes. Presented examples are based
on the experience of students’ research
works and serve as a link between initial
stage and studies on the basis of
complicated
professional
industrial
commercial codes for preliminary stage of
the modeling.
NOMENCLATURE
H
T

g


a


Т
Gr
Mn
Pr
length scale
temperature scale
tension factor on a free surface
gravity acceleration
density
thermal conductivity
heat transfer coefficient
kinematics viscosity
thermal diffusivity
thermal expansion coefficient
Grashof number, Т T g·H3/2
Marangoni number,
(d/dT) (T·H)/(·)
Prandtl number, /a
1. INTRODUCTION
Computational Fluid Dynamics (CFD) is
important instrument for investigation
transfer phenomena of fluid and has a huge
range of the applications. However a
problem how to find an efficient way to the
access to this instrument is actual because
of elementary flows and heat/mass transfer
processes in realistic industrial applications
are nonlinear, unsteady, multi parametric
and multi scale. A number of the books and
textbooks devoted to the fundamentals of
the fluid mechanics and applications in heat
and mass transfer discuss the problem (see,
for instance, [1-5]). Last decades efficient
professional tools for modelling on the
basis of Navier-Stokes equations and the
industrial complexes of programs are
developed. They have a number of the
tutorials, which mainly oriented for the
users guide, following complicated
instructions. Development of the numerical
heat transfer needs intermediate systems,
which help to access to the scientific nature
of the problems for education process with
the use of the modern tools of the
modelling for new generation of
researchers. One can find one of the first
steps on the basis of one-dimensional and
boundary layer type approach oriented on
the engineering education, using Mathcad
[5]. Education and tutorials in modelling of
the elementary flows on the basis of
Navier-Stokes equations in ground-based
and microgravity environments using
computer system COMGA (COnvection in
MicroGravity and Applications) and
ASTRA
(Automated
System
for
Theoretical Research and Analysis) are
developed and based on the previous
4th International Conference on Computational Heat and Mass Transfer
experience of the modelling [6,7].
Computer laboratory as intellectual shell of
these systems includes microgravity and
ground-based applications [6]. Basic
tutorials of fluid dynamics and heat/mass
transfer such as hydrostatic equilibrium,
stability of the steady flow, study of the
elementary of the buoyancy-driven,
surface-tension gradients driven and forced
convective flows and multi-parametric
analysis and some applied tutorials for
microgravity
fluid
mechanics
and
technological fluid dynamics presented in
[8, 9, 12].
In this paper a plan of the education and
tutorials for convective heat/mass transfer
processes on the basis of Navier-Stokes
equation from preliminary stage of the
modelling with a link to the comprehensive
commercial codes similar [10] is presented.
2. COMPUTER EDUCATION USING
MATHCAD SYSTEM
The understanding of the general
engineering problem is very important point
for initial stage of the education.
Engineering-physical projects executed in
Mathcad include problem-setting and
physical model formulation, designing on
the basis of one-dimension or boundary
layer-type of models [5] (www.thermal ru).
The initial step shows on real examples
how to use effectively Mathcad at all
development stage of an engineering
project (analytical preprocessing the
mathematical
description
(during
normalization, research of the special
points, identical transformations, etc.),
analytical decisions where it the
opportunities of symbolical Mathcadprocessor allows, the numerical decision
when analytical decisions are impossible or
inefficient, results
presentation
and
visualization.
3. EDUCATION & TUTORIAL IN
MODELING ON THE BASIS OF
NAVIER-STOKES EQUATIONS
Next step of the education may be study
and tutorials using relatively small
computer systems as COMGA, ASTRA
[6-7]. The COMGA system (see
www.ipmnet.ru/~ermakov)
supports
modeling problems of free and forced
convection on the basis of the NavierStokes equations (Boussinesq approach). A
basic version of the system and computer
laboratory includes classical problem of
convective heat and mass transfer with
different types of the boundary conditions,
external forces and fluid (gas) properties. In
Fig.1 general classification of the
elementary convective processes of the
gravity- and non gravity types which
contains such kind of computer laboratory
is shown.
Fig 1. Classification of the elementary 2D
convection and heat/mass transfer processes
Classification deals with the convection
problems in an enclosure with rigid (solid
lines) or free boundaries (dashed line) in the
field of gravity (g), vibration and slow
rotation for binary mixture (heat and mass
transfer). Solid arrows show direction of the
heat flux, dashed arrows are direction of the
mass flux. First four items correspond to
the case, when mechanical equilibrium
exists in uniform (two first) or binary (third
and forth) systems. Two last items
correspond to the case of advection –
convection which induced by the horizontal
temperature or concentration gradient
which are gown in the same or in opposite
directions. Four intermediate items
correspond to the coupling between
stratified and advective flows. It should be
taken into account multidimensional nature
of the convection and possibility to provide
for students an experience in simplest
parametrical analysis of the searched
characteristics of heat/mass transfer.
Computation
code
ASTRA
(www.ipmnet.ru/~burago)
similar
elementary items also contains (Fig2).
Using
adaptive
Eulerian-Lagrangian
4th International Conference on Computational Heat and Mass Transfer
unstructured grids and the finite element
method, ASTRA provides numerical
solution of the one, two and three
Fig. 2. ASTRA computer system as efficient
tool for education of the elementary heat mass
transfer processes
dimensional unsteady nonlinear problems
in continuum (fluid and solid) mechanics.
ASTRA’s distinguishing features are as online preprocessors for generation of
unstructured finite element grids in two and
three dimensional regions; on-line editor for
preparation of the geometrical and physical
starting
data.
Free
format
rules
(NAMELIST style), online help for
keywords and online diagnostics of errors
facilitate this part of job; on-line symbolic
debugger for providing detail analysis and
management of data, breakpoints, dumping,
restart etc; an inbuilt postprocessor for online visualization of the results in form of
tables, graphs, contour lines, colour zones.
With ASTRA it is easy to produce movies
and to perform hard copies of pictures in
PCL, HPGL or PostScript formats;
possibility of modification and replacement
of the code component. Source code of
problem orientated part of ASTRA and
high level software for pre- and postprocessing are opened for interested users.
Basic education and tutorials
Initial stage of education with the use of the
COMGA, ASTRA can be start from the
definition of the physical properties of the
typical liquids and gases, hydrostatic
equilibrium, driving forces, induced by the
buoyancy and gradient of the surface
tension (Marangoni) as wall as general
reasons for onset of convection and
convective instability. It is necessary to
note, that a first step of preparation can be
acquaintance of learning colleges and
universities with classical experimental
results and with the elementary analytical
exact solutions of the equations of
conduction and hydrodynamics (Poiseuille
flow in a pipe, boundary layer Blaziuse
flow on a plate, slow convection flows in
layers etc.)
Elements of the modeling theory as well as
the basic knowledge of numerical methods
should be done for understanding the
options of the FDM, FEM methods. For
instance, some versions of the implicit
scheme for viscous terms, second-order
approximation applied on staggered mesh,
FFT method for the pressure correction
step, significance of the uniform (non
uniform) meshes with approximation of the
Navier-Stokes
equations
should
be
explained.
Starting from the elements of the
convection tutorials, classical problems of
the gravity-driven convection with side
heating, Rayleigh-Benard convection with
rigid and free melt surfaces, and similar
types of the Marangoni convection will be
studied.
Fig. 3. Example of the tutorial for the onset of
Marangoni convection in a layer with free
surface and bottom heating. Menu of the basic
part of the computer laboratory.
A fragment of problem solution on thermocapillary convection in horizontal layer
during
bottom
heating
(Marangoni
instability), presented in Fig. 3, illustrates
onset of Marangoni convection after the
loss of hydrostatic equilibrium stability and
formation of the steady state regime for the
4th International Conference on Computational Heat and Mass Transfer
classical Pearson problem [11]. Stream
functions illustrate roll structure on the top
and
isotherms
of
thermo-capillary
convection - below. On the right side in
middle a temporal evaluation of the
maximum of stream function is shown. A
fragment of Menu of computer system
COMGA_W is shown on the left side. One
can see here a title of the problem and items
inside a "Problem category", which only a
given problem characterizes: parameters
Mn, Pr, region L/H, body force (g=0 in this
case) and type of initial conditions. The
menu makes it possible also to change mesh
size, visualization type, or to use
information from a file. Following the
classification in Fig. 1 most of the
elementary convective problems can be
studied and illustrate in real time
calculation processes by the students during
the tutorial process.
Therefore the basic tutorial can make
support of the number textbooks on heat
transfer and fluid mechanics and convective
stability [1, 4]. A number of examples
which discussed in a monograph [5] can be
solved again and illustrate in details. Note
that complex experimental and computer
tutorial [8] is also important step on this
way as a link with concrete physical nature
and validation of the computer modeling
results.
Basic
tutorial
with
technology
applications
Special versions of the systems COMGA
and ASTRA were developed for the cases
of technology geometries and microgravity
environment [6, 12]. Possibility of
computer laboratory for study fluid flow
and heat transfer in technology applications
may be explain on hydrodynamics (or socalled idealized) Czochralski model, which
represents a nonlinear multi parametrical
hydrodynamic system with wide range
values of governing parameters. It‘s control
function (for instance, amplitude of
temperature oscillation, A) seems as
follows:
A = f (r, z, φ, Res, Rec, Gr, Mn, Pr, Rs/Rc,
H/Rc, γ1, γ2)
(*)
Here Res, Rec – are two dynamical criteria:
Reynolds numbers related to the seed and
crucible rotation (forced convection). Gr,
Mn – are two natural convection criteria –
Grashof and Marangoni numbers, Pr
number - is a criteria of the physical
properties, H/Rc, Rs/Rc – are two
geometrical parameters - non dimensional
height of the melt and width of the seed,
and γ1, γ2 – are thermal boundary and initial
conditions. One part of the tutorial (see
more information in [12]) consists with a
number of examples deals with typical
crystal growth configurations for silicon,
GaAs, oxides melts and other kinds of the
crystal growth on the basis of the axissymmetric model following the paper [13].
Fig. 4. Simulation by system INTEX regimes of
coupling convection and crucible rotation
visualized by temperature (left) and stream
function (right) fields. Res=0, Mn =0,
Gr=7.8 107,
Pr=0.07,
H=Rc=Rs/Rc=0.578,
4
a) Rec =1.6 10 , b) Rec=1.9 103, c) Rec=103
Formulation (*) shows principal possibility
for control of fluid flow/temperature fields
in the melt using thermal (power input,
including boundary condition), dynamical
(steady state crystal/crucible rotation or
angular acceleration, artificial vibration
etc.) geometrical (dimensionless melt level
or width of the melt surface) and gravity
level control. Fig. 4 illustrates possibilities
of the parametric analysis of the coupling
between gravity driven convection and fluid
flow induced by the crucible rotation.
Crucible rotation induces the temperature
oscillation in the melt for typical GaAs
parameters [13] which may be reduced by
the lower rotation rates.
4th International Conference on Computational Heat and Mass Transfer
4. A LINK BETWEEN COMGA,
ASTRA and FLUENT TUTORIALS
Above mentioned tutorials make it possible
to understand some elementary convective
processes deals with more complicated
process. Next step on the way of training of
the students can be mastering by a package
FLOWLAB [10], giving an opportunity in a
uniform package will familiarize with all
chain of process of modeling of tasks CFD.
During work with this package, the user
FLOWLAB, will familiarize. First, with
elementary principles CAD system of
construction of geometrical bodies (which
will be useful to any engineer going to
work with professional CAD by the
programs, (for example, such as
Pro/ENGINEER, I-DEAS, CATJA V4,
UNIGRAFICS and etc.) secondly, with
application of the generator of grids,
thirdly, with solver, and, fourthly, about a
post-processing and elements of the
analysis of numerical results.
An example of the FLUENT tutorial which
deals with modeling solidifications
(following tutorial No 20 “solid” [10])
illustrates how to set up and solve a
problem involving solidification. In this
tutorial, you will learn how to define a
solidification
problem,
define
pull
velocities for simulation of continuous
casting, define a surface tension gradient
for Marangoni convection and solve a
solidification problem. This tutorial
assumes that users are familiar with the
menu structure in FLUENT, and that you
have solved previous tutorials. Some steps
in the setup and solution procedure will not
be shown explicitly. It demonstrates the
setup and solution procedure for a fluid
flow and heat transfer problem involving
solidification, namely the Czochralski
growth process. The geometry considered is
a 2D axisymmetric bowl, containing a
liquid metal, free surface, mushy zone and
crystal in Fig 5). The bottom and sides of
the bowl are heated above the liquidus
temperature, as is the free surface of the
liquid. The liquid is solidified by heat loss
from the crystal and the solid is pulled out
of the domain at a rate of 0.001 m/s and a
temperature of 500 K. There is a steady
injection of liquid at the bottom of the bowl
with a velocity of 1.01x10-3 and a
temperature of 1300 K. Material properties
are corresponded to semiconductor. Starting
with an existing 2D mesh, the details
regarding the setup and solution procedure
for the solidification problem are presented.
Fig. 5. Simulation flow in Czohralski Crystal
Growth by using FLUENT. Contours of
temperature (left) and stream function (right) in
moment time t=22 sec.
Then, the fluid flow is turned on to
investigate the effect of natural and
Marangoni convection in an unsteady
fashion with able moving solid-liquid
interface. The results of calculation of flow
and heat transfer in Czochralski Crystal
Growth carried out by authors using
FLUENT is showed for moment t=22 sec in
Fig. 5. Dynamical changing of the structure
of flow and relocation of interface user also
can to show using animation options. If it
needs user can to change of values of
parameters, properties of the problem,
tested of different physical and numerical
models on one tutorial, but for correct using
the models he must has introductory
knowledge about that and to be able rightly
to apply these models. For that preliminary
training computer laboratory similar
COMGA, ASTRA FLOWLAB program
can be efficient tools.
CONCLUSIONS
Presented plan of the education and tutorials
is oriented mainly on the convective
processes and heat transfer and applications
and suppose before the study industrial
packages tutorials (see for instance [10])
preliminary stage of education as follows:
1. Basic Heat Mass Transfer Educations,
Fluid Mechanics and Engineering
education textbooks [1 -5].
2. Computer laboratories [6, 8, 12] for the
4th International Conference on Computational Heat and Mass Transfer
elementary convective flows which
supports of the above mentioned fluid
mechanics and heat/mass transfer
textbooks.
3. Complex tutorials [10] of the
professional industrial code, for example,
FLUENT.
Note, that computation methods and solvers
techniques extremely rise during last years,
but most of them are outside of the
computer laboratories now. For instance,
efficient codes for DNS problems,
including direct simulation of the stability
and turbulence, three dimensional stability
[13-14], a hierarchy of compressible fluid
flow models including near critical ones
[15] and a number of the new applied
problems will be included in the education
process in the near future.
ACKNOWLEDGEMENTS
This work are supported partly by RFBR
grants 03 01- 0682, RFBR - NSFC № 0401-39021, a well as project ”Integratziya”
by the Ministry of Education of Russian
Federation by the guidance of Rostov State
University No. 74. The authors express
their gratitude to the Prof. A.P. Solodov for
the information related engineering
education,
Prof.
N.G.Bourago,
Dr.
M.K.Ermakov and S.A.Nikitin for the
access to the ASTRA, COMGA and
INTEX systems and to the company
“Processflow Inc.” for the opportunity of
the use the program FLUENT.
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